Convexity for invariant differential operators on semisimple symmetric spaces
These are the lecture notes of a minicourse given at a winter school in Marseille 2011. The aim of the course was to give an introduction to recent work on the geometry of the space of Kähler metrics associated to an ample line bundle. The emphasis of the course was the role of convexity, both as a motivating example and as a tool.
We write a cohomological resolution of the sheaf of solutions of the differential operator on a manifold and study the cohomology groups and .